1994 corolla: hard to start

Out of gap spark plugs or leaking plug boots positive spark is getting to ground stopping all plugs from firing properly or to large a gap in plugs I'm assuming that you mean the engine e is cranking but not turning over fast and persistent cranking finally starts it

How to Start a Car in Freezing Cold Winter Weather

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wikiHowFreezing cold weather can take a toll on car batteries. ... It's much more difficult to start a cold car with a mostly-empty tank, so do yourself a favor and gas up ...

Why is it so hard to start a car in the winter? - HowStuffWorks

auto.howstuffworks.com/car-driving-safety/.../start-car-in-winter.htm

To start a car in winter, your engine has to work extra hard. Learn the top 3 reasons your car is hard to start in cold winter weather.

Debunking 5 Cold-Weather Car Myths - Popular Mechanics

new spark wires. old wires hate, cold damp weather.
spark plugs, cap,rotor wires, try the 60k mile tuneup. per the opr.guide.
magic happens....
the map is ok.
and to test a map you need the graph and you need to compensate for altitude and local weather (barometer readings) to correct what you see.
is the check engine light glowing running?
most maps read like this, 1bar maps.
http://www.fixkick.com/sensors/my-map.html#Jeep

i bet your's is ok. the map.
your car is a toyota corolla in snake clothing.
the toy FSM covers this is find details.

this will happen as it gets colder.. preheater needs to reach temperature before starting..in really cold weather we used to turn the key on and off a half dozen times in order to get these glowplugs really warm enough to start these diesel trucks..

Batteries, when cold, are not able to provide anything near their rated power output. Engines, when cold, require much more torque to turn over than when warm. Starters, when cold, require much more current to operate. Older batteries have less reserve starting power. Battery chargers will restore voltage levels, over time, but are not the same as a battery or "jump start". Add it up. Cold motor hard to turn over. Cold starter demanding more power to run itself, plus even more to turn cold motor. Battery at its weakest due to cold. Chances are the battery needs replacement.

You could be right, it may not be the battery, but something to consider.
In cold weather the damand on the battery to turn and start the engine is much higher than in warm weather.

Often people buy a replacement battery without knowing what the minimum, "cold cranking amps," rating is for their car. And often there's no sign of any problem. But, when the weather turns cold not having the minimum cold cranking amps is now a problem.

Just as a procautionary measure, you could read the cold cranking amps rating on your battery, and then call any parts store to see what battery is called for as a replacement. This could prove very helpful.

Something else that may be helpful to you.

1. You could check on your battery to see if it is a maintenance free battery.
If it's not maintenance free, you should have the levels in your battery checked. If the levels are low it will prevent the alternator from charging the battery up to its peak level.

I hope this helps.

I WOULD HAVE BATTERY TESTED.BATTERYS ARE KNOWN TO DIE IN COLD WEATHER,ESPECIALLY IF THE BATTERY IS COUPLE OF YEARS OLD

Check your battery for proper volts (12.6). Sometimes the cold weather will bring a battery down. Also check the Starter Relay, again cold weather will make it stick causing it not to start. Those are the biggest problems with a car not starting in the cold weather unless you have something else going on then your starter and your ignition needs to be checked.

the car doesnt come with a timing belt, it has a 10 year worry free, internal timing chain, but it sounds like either your battery or starter, cold weather causes the electric flow to slow down, take your battery in to see if its ok, then check your starter. good luck and hope this helps

Radio and lights can work with weak battery, too weak to turn starter.

Noise when shutting off maybe dieseling due to fuel mixture too rich or timing off.

When you say car won't start do you mean starter turns but engine does not start, or do you mean starter does not turn.